In this paper we consider the optimal dividend strategy under the diffusion model with regime switching. In contrast to the classical risk theory, the dividends can only be paid at the arrival times of a Poisson process. By solving an auxiliary optimal problem we show that the optimal strategy is the modulated barrier strategy. The value function can be obtained by iteration or by solving the system of differential equations. We also provide a numerical example to illustrate the effects of the restriction on the timing of the payment of dividends.
"On the optimal dividend strategy in a regime-switching diffusion model." Adv. in Appl. Probab. 44 (3) 886 - 906, September 2012. https://doi.org/10.1239/aap/1346955269